Index laws

• Multiplication when the base is the same:
  \[a^m \times a^n = a^{m+n}\]
• Division when the base is the same:
  \[ a^m \div a^n = \frac{a^m}{a^n} = a^{m-n}\]
• Power of power rule:
  \[ (a^m)^n = a^{m\times n}\]
• Power of a product rule:
  \[ (ab)^m = a^m \times b^m\]
• Fractional power notation:
  \[ a^\frac{m}{n} = \sqrt[n]{a^m}\]
• The zero index:
  \[a^0 = 1\]
• The negative index:
  \[ a^{-m}= \frac{1}{a^m}\]